Measuring consensus effectiveness by a generalized entropy criterion

A quantitative criterion for measuring the effectiveness of the consensus obtained by pooling evidence from two knowledge sources is introduced. A brief review of the Dempster-Shafer theory of mathematical evidence, which is based on a set-theoretic description of subjective uncertainty, is given. The concept of generalized entropy as a measure of the uncertainty in a knowledge source is also introduced. It is proven that the pooling of evidence by Dempster´s rule of combination decreases the total amount of generalized entropy in the knowledge sources. The decrease of entropy corresponds to the focusing of knowledge, and is used as a measure of consensus effectiveness. Several examples are used to illustrate this measure